Answer:
a) P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
b) P(6) = 7,805\ millionP(6)=7,805 million
c) t = 14.64\ yearst=14.64 years
d) t = 24.15\ yearst=24.15 years
Step-by-step explanation:
a) The function of exponential growth for a population has the following formula:
P(t) = p_0e ^{rt}P(t)=p
0
e
rt
In this equation:
p_0p
0
is the initial population
r is the growth rate
t is the time in years
In this problem we know that
r = 2.87\% = 0.0287r=2.87%=0.0287
p_0= 6.57p
0
=6.57 million in the year 2012.
So the equation is:
P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
Where t = 0t=0 represents the year 2012
b) If t = 0t=0 in 2012, then in 2018 t = 6t=6
The population in 2018 is:
\begin{gathered}P(t = 6) = 6.57e ^{0.0287(6)}\\\\P(6) = 7,805\ million\end{gathered}
P(t=6)=6.57e
0.0287(6)
P(6)=7,805 million
c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.
\begin{gathered}P(t) = 10 = 6.57e ^{0.0287t}\\\\\frac{10}{6.57} = e ^{0.0287t}\\\\ln(\frac{10}{6.57}) = 0.0287t\\\\t = \frac{ln(\frac{10}{6.57})}{0.0287}\end{gathered}
P(t)=10=6.57e
0.0287t
6.57
10
=e
0.0287t
ln(
6.57
10
)=0.0287t
t=
0.0287
ln(
6.57
10
)
t = 14.64\ yearst=14.64 years
d) The function is doubled when P(t) = 2p_0P(t)=2p
0
P(t) = 2(6.57) = 13.14 = 6.57e ^{0.0287t}P(t)=2(6.57)=13.14=6.57e
0.0287t
We solve for t.
\begin{gathered}\frac{13.14}{6.57} = e ^{0.0287t}\\\\ln(\frac{13.14}{6.57}) = 0.0287t\\\\t = ln{13.14}{6.57})}{0.0287})\
end
{gathered}
6.57
13.14
=e
0.0287t
ln(
6.57
13.14
)=0.0287t
t=
0.0287
ln(
6.57
13.14
)
)
t = 24.15\ yearst=24.15 years
What is the domain of the relation [(x,y):y=x(x-3)/(x+4)(x-7)
Answer:
i think its b
Step-by-step explanation:
Find the product 822x9=
Answer:
7398
Step-by-step explanation:
Answer:
7398
I mean, this is the answer. You COULD just use a calculator, but here.
Glad I can help. :)
Please help me!!!!!
Answer:
The answer is A.
Step-by-step explanation:
The ratio is 1 second/2 centimeters, but since they're asking for a unit ratio, you need to divide the top and bottom by 2 which gives you a unit ratio of ½ second/1 centimeter.
Answer:
Perhaps, B or A
Step-by-step explanation:
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
Find the slope of the line that passes through the points (–2, 4) and (5, 4).
Answer:
slope is 0
Step-by-step explanation:
Answer:
slope is 0
Step-by-step explanation:
I used another app to find the awnser for you
I NEED THE ANSWER QUICK
9514 1404 393
Answer:
4^0
Step-by-step explanation:
The rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
So, your expression simplifies to ...
[tex]4^5\times4^{-7}\div4^{-2}=4^{5-7-(-2)}=\boxed{4^0}[/tex]
Please need help thank
Answer:
35 balloons
Step-by-step explanation:
If wrong srry...hope this helps
Answer:
35 bunches
Step-by-step explanation:
25*7=175 balloons
5 balloons in each bunch=175/5
=35
An item on sale cost 35%of the original price. The original price was $25. What was the sale price?
[tex]{\underline{\pink{\textsf{\textbf{ Answer : }}}}}[/tex]
➩ $33.75
[tex]{\underline{\purple{\textsf{\textbf{ Explanation : }}}}}[/tex]
Original price of the item is $25
As it told that it costs 35% of the original price
Therefore
➡ $25 + (35% of 25)
➡ $25 + 8.75
➡ $33.75 ans.
Answer: 8.75
Step-by-step explanation:
i got it wrong this is what the test showed as the real answer
If a bike has a sale price of $6 what was the original price if she pays 60% off original price
Answer:$15
Step-by-step explanation:$6=30% 6/3=$1.5*10=$15
Find the circumference of a circle with a radius of
6 cm
Answer:
C = 12π cm
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASGeometry
Circumference: C = 2πrStep-by-step explanation:
Step 1: Define
Radius r = 6 cm
Step 2: Find C
Substitute: C = 2π(6)Multiply: C = 12πRound 61.7625 to the neares
Answer:
Nearest whole: 62
Nearest tenth: 61.8
Nearest hundredths: 61.76
Nearest thousandths: 61.763
Cole's soup recipe is shown in the table above. What is the ratio of water to chicken stock? Express the ratio as a fraction in simplest form.
Answer:
2:3
Step-by-step explanation:
4:6, you would have to divide both sides by 2 to get the simplest answer which is 2:3, hope this helps
2. What number is equal to five units + three tenths? Circle the correct answer.
0.53
0.35
5.3
3.5
53
35
Answer:
35
Step-by-step explanation:
5*1+3*10
5+30 = 35
29.9.2+ n+ 8.4 = 20.8
Please help
Answer:
n=6.42
Step-by-step explanation:
Following the steps for this equation.
Answer:
29.9.2+
Step-by-step explanation:
That should be right
If you have two nickels and two dimes and nine pennies how much will that be
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of
Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation of the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.
Therefore:
The expected value of the sampling distribution is equal to the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The shape of the sampling distribution of
¯
x
is approximately normal. As the sample size is more than
30
.
3) The probability that the average life in the sample will be between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability that the average life in the sample will be greater than
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
Using Excel: =NORMSDIST(-1.89)
5) The probability that the average life in the sample will be less than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
The expected value, standard deviation, and shape of the sampling distribution of will be 116.
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Now,
Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Hence, The expected value, standard deviation, and shape of the sampling distribution of is,
⇒ Standard error = 696 / √ 36
= 696 / 6
= 116
Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ5
What is the equation for the line that passes through (3, 2) and has a slope
equal to 12
3
Answer:
Step-by-step explanation:
Remark
I'm not sure I know what you intend for the slope. I will take it as 12/3 = 4
If that is the case then what you have so far is
Solution
y = 4x + b
The given point determines b
Givens
x = 3
y = 2
Given point
2 = 4*3 + b
2 = 12 + b
b = 2 - 12
b = -10
The equation is y = 4x - 10
Given the cos(θ) = 5/13 the ratio for sine of θ is
. Enter your answer as a fraction.
1) Escribe cuatro nombres para la rectaIJ
2) Nombra 3 segmentos de recta distintos que estén sobre HF.
3) Nombra 5 rayos que tengan el mismo extremo.
4) ¿Son BD y DB el mismo rayo? Explica si son el mismo rayo.
Answer:
GeraldineLucero Mejia Castillo,Magda CamanCastro,AnibalUlises Galiano Grados,Juan David
Step-by-step explanation:
ojala que te cirva
Hey! Just do the first one! :) I also need this fast- so help! :((
Answer:
the second one
Step-by-step explanation:
that's the answer
I need help please : )
Answer:
i think the answer is 10x^3-12^2-198x-40
Mrs. Garcia deposited $2500 into a new bank account. The bank pays 1.5% interest compounded annually on this account. She makes no additional deposits or withdrawals. How much is in her account at the end of 2 years?
Step-by-step explanation pls! :)
Answer:
$2575.5625
Step-by-step explanation:
2500*(1.015)^2
=$2575.5625
PLS GIVE BRAINLIEST
1st Year 2500*1.015=2537.5
2nd Year 2537.5*1.015=2575.5625
Write these following fractions in order from greatest to least
1/9
1/2
1/8
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] \frac{1}{9} = \frac{1 \times 8}{9 \times 8} = \frac{8}{72} \\ [/tex]
[tex] \frac{1}{2} = \frac{1 \times 36}{2 \times 36} = \frac{36}{72} \\ [/tex]
[tex] \frac{1}{8} = \frac{1 \times 9}{8 \times 9} = \frac{9}{72} \\ [/tex]
_________________________________
[tex] \frac{8}{72} < \frac{9}{72} < \frac{36}{72} \\ [/tex]
[tex] \frac{1}{9} < \frac{1}{8} < \frac{1}{2} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Thus the order from greatest to least is :
[tex] \frac{1}{2} \: , \: \frac{1}{8} \: , \: \frac{1}{9} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
8=1/4(x+16) in simplest form
Answer:
X = 16
Step-by-step explanation:
multiply 1\4 by (x+16)
u got 8 = 1\4x +4
32 = x + 16
-x = -16
so x = 16
Hope you got it.
Mark it as Brainliest .
Answer:
x=16
Step-by-step explanation:
I HOPE THIS HELP
A local Little league has a total of 60 players, 80% of whom are right-handed. How many right-handed players are there?
(Please answer step by step.)
Answer:
48 right-handed players
Step-by-step explanation:
first, make an equation
[tex]\frac{80}{100} =\frac{x}{60}[/tex]
then, cross multiply and the new equation is
[tex]100x=4800[/tex]
finally, divide by 100 on both sides to isolate the x and you get
x=48
An asteroid and a planet are 383 000 km apart.
The asteroid then travels 99 500 km towards the planet.
How far does the asteroid have left to travel before
it reaches the planet? Work it out in your head.
Answer:
283500
Step-by-step explanation:
Your answer is
[tex]383000-99500[/tex]
Which is 283500
Hope this helps Please hit the crown :D
The asteroid are separated by 383,000 km.
The asteroid moves 99,500 km toward the planet.
Let F = how far does the asteroid need to travel before reaching the planet.
F = 383,000 km - 99,0m500 km
F = 283,500 km
Got it?
What is the value of a? Please solve this with the law of sine
Answer:
what chap is this
Step-by-step explanation:
Please help I’ll mark brainliest if u give a small explanation!!!
Answer:
ut is a if you add 5 plus 4 it makes 9 do not add the 8
Hailey is going to use a computer at a Internet cafe. The cafe charges $1.50 for every minute using a computer on top of an initial charge of $4. Make a table of values and then write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the Internet cafe.
Answer:
The equation is C(t) = 1.50t + 4.00 and the data table is below.
Step-by-step explanation:
We are given that a cafe charges $1.50 for every minute that someone uses the internet. The cafe also charges an initial $4 fee to use the internet.
We need to find a function, in terms of t, that will find these values.
We can treat this as a linear equation. If we initially pay $4, this is acquired before we pay the fee every minute. Therefore, this would be our y-intercept at x = 0. Our first coordinate is (0, 4).
Secondly, if we are charged every minute, this would be a recurring payment and therefore we would spend $1.50 after each minute elapses. This gives us our slope: 1.50 or [tex]\frac{3}{2}[/tex].
Therefore, we can set up our function.
C is the total cost and t is the time, in minutes, that internet is used at the cafe. Our equation can be set up as [tex]C(t) = 1.50t + 4.00[/tex].
Now, we can create a table of values for t = 0 to t = 5 to determine what C(t) is at each of these prime intervals.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} a & 0 \\ \cline{1-2} b & 1 \\ \cline{1-2} c & 2 \\ \cline{1-2} d & 3 \\ \cline{1-2} e & 4 \\ \cline{1-2} f & 5 \\ \cline{1-2} \end{array}[/tex]
This is what our table looks like, but we need to fill the C column. Therefore, we can use substitution of our t-values into the equation and solve for C.
[tex]\bullet \ \text{For t = 0,}[/tex]
[tex]C(0) = 1.50(0) + 4\\\\C(0) = 0 + 4\\\\C(0) = 4.00[/tex]
[tex]\bullet \ \text{For t = 1,}[/tex]
[tex]C(1) = 1.50(1) +4\\\\C(1) = 1.50 + 4\\\\C(1) = 5.50[/tex]
[tex]\bullet \ \text{For t = 2,}[/tex]
[tex]C(2) = 1.50(2) + 4\\\\C(2) = 3.00 + 4\\\\C(2) = 7.00[/tex]
[tex]\bullet \ \text{For t = 3,}[/tex]
[tex]C(3) = 1.50(3) + 4\\\\C(3) = 4.50 + 4\\\\C(3) = 8.50[/tex]
[tex]\bullet \ \text{For t = 4,}[/tex]
[tex]C(4) = 1.50(4) + 4\\\\C(4) = 6.00 + 4\\\\C(4) = 10.00[/tex]
[tex]\bullet \ \text{For t = 5,}[/tex]
[tex]C(5) = 1.50(5) + 4\\\\C(5) = 7.50 + 4\\\\C(5) = 11.50[/tex]
Now, we can insert these values into our table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} 4.00 & 0 \\ \cline{1-2} 5.50 & 1 \\ \cline{1-2} 7.00 & 2 \\ \cline{1-2} 8.50 & 3 \\ \cline{1-2} 10.00 & 4 \\ \cline{1-2} 11.50 & 5 \\ \cline{1-2} \end{array}[/tex]
Therefore, our equation is C(t) = 1.50t + 4.00 and our data table is above.
Abigail has $400 in her savings account. She wants to keep at least $160 in the account.
She withdraws $40 each week for food. Write and solve an inequality to show how many
weeks she can make withdrawals from her account.
Answer:
400-40x x=6
Step-by-step explanation:
400 in total. minus 40 each week (x)
40 × 6= 240
400-240=160
A 12-oz box of cereal costs $1.68.
What is the cost per Ounce?